NOTE: The parameters considered by @Mulletron, under all cases considered (including Earth to Saturn in 757 days or 25.2 months) are safely under the "paradox condition" of Joosten/White. There is no paradox for these Mulletron Missions: the change in kinetic energy is less than the energy consumed

The "paradox condition" of Joosten/White for the parameters considered by @Mulletron occurs at 910 days (30.3 months of continuous acceleration).

The "paradox condition" is defined as the condition for which the change in kinetic energy of the spacecraft exceeds the input energy.

Maybe not the brightest of questions, but could Doctor McCulloch's theory possibly resolve the paradox issue? Accelerate long enough, and inertial radiation becomes significant?

NOTE: The parameters considered by @Mulletron, under all cases considered (including Earth to Saturn in 757 days or 25.2 months) are safely under the "paradox condition" of Joosten/White. There is no paradox for these Mulletron Missions: the change in kinetic energy is less than the energy consumed

The "paradox condition" of Joosten/White for the parameters considered by @Mulletron occurs at 910 days (30.3 months of continuous acceleration).

The "paradox condition" is defined as the condition for which the change in kinetic energy of the spacecraft exceeds the input energy.

Maybe not the brightest of questions, but could Doctor McCulloch's theory possibly resolve the paradox issue? Accelerate long enough, and inertial radiation becomes significant?

I don't think so. The paradox occurs under conditions of constant acceleration. Under constant acceleration, the Unruh radiation stays the same in McCulloch's theory. (Ditto for Hawking radiation under constant acceleration).

The paradox occurs under constant acceleration when the velocity exceeds 2 times the PowerInput divided by the thrust force, since that implies a change in kinetic energy greater than the energy provided.

Just a thought, but the higher the Q, the narrower the bandwidth, and the Doppler shift due to actual acceleration (or velocity in the rest frame) would probably limit that amount by exceeding the bandwidth.

Just a thought, but the higher the Q, the narrower the bandwidth, and the Doppler shift due to actual acceleration (or velocity in the rest frame) would probably limit that amount by exceeding the bandwidth.

To all, let's recall that

ThrustForce/PowerInput ~ Q*otherParameters

in all the formulas (Shawyer's, McCulloch's and NotSoSureOfIt's). (NotSoSureOfIt's formula also depends explicitly on the microwave's cavity mode of operation).

Thereforethe maximum velocity of the EM Drive is inversely proportional to Q:

At constant input power, the thrust, and therefore the acceleration, must decrease with time, to ensure that the spacecraft's velocity never exceeds 2*Power/Thrust

I was going to start a thread, but there is a photon rocket variant idea I have been batting around for a few months now:

take a long hollow cylinder, closed at one end, open on the other. Probably several hundred meters long, by three or four meters in diameter. Running the length of this cylinder, spaced at even intervals are low beams - probably no more than ten or twenty centimeters high. So the inner edge of the cylinder has...call it a dozen shallow troughs. At regular intervals - maybe a meter - these beams have specially designed reflective points. Open end of the cylinder, you have a powerful high frequency laser (or something emitting a focused photon beam) aimed at a 45 degree angle into each trough. One laser per trough, call it twelve total.

Now, a laser, like a military searchlight, is also a photon rocket.

Photons, as pointed out in the previous thread are durable little critters, and can bounce around a good 50,000+ times before going wherever it is expired photons go. And photons can transfer momentum with each bounce.

So, turn the lasers on. The initial 'thrust' is backward. Actually, 'backward and sideways' because of the angle.

That thrust gets negated at the first bounce point. Photons hit that (reflective) point, transfer momentum, and head over to the next bounce point, set at a 45 degree angle to the first.

At the second bounce point, the whole thing is moving forward. Repeat for the length of the cylinder. Because the photons are hitting at an angle, the cylinder might start rotating as well as moving forward, but I don't see that as a major issue. At the end of the cylinder, the photons hit a shaped surface and bounce back along the tubes center and out into space.

Did a bit of reading on laser propulsion systems. A Doctor Bae ran some laboratory tests on this: bouncing laser beams multiplied the 'thrust' by a factor of 3000+ - into EM Drive territory without the physics headache. He proposed two linked spacecraft, with laser beams between them, something NASA is supposed to be looking into for near earth applications. My idea is one spacecraft (the cylinder) and a multiplier of about 1500, if the cylinder is long enough. Not sure, but that's should be on a par with the Brady EM drive model.

Alter the angles a bit, test different lasers/emitters, might get a lot more work out of the photons, increasing thrust further.

At constant input power, the thrust, and therefore the acceleration, must decrease with time, to ensure that the spacecraft's velocity never exceeds 2*Power/Thrust

I was going to start a thread, but there is a photon rocket variant idea I have been batting around for a few months now:

take a long hollow cylinder, closed at one end, open on the other. Probably several hundred meters long, by three or four meters in diameter. Running the length of this cylinder, spaced at even intervals are low beams - probably no more than ten or twenty centimeters high. So the inner edge of the cylinder has...call it a dozen shallow troughs. At regular intervals - maybe a meter - these beams have specially designed reflective points. Open end of the cylinder, you have a powerful high frequency laser (or something emitting a focused photon beam) aimed at a 45 degree angle into each trough. One laser per trough, call it twelve total.

Now, a laser, like a military searchlight, is also a photon rocket.

Photons, as pointed out in the previous thread are durable little critters, and can bounce around a good 50,000+ times before going wherever it is expired photons go. And photons can transfer momentum with each bounce.

So, turn the lasers on. The initial 'thrust' is backward. Actually, 'backward and sideways' because of the angle.

That thrust gets negated at the first bounce point. Photons hit that (reflective) point, transfer momentum, and head over to the next bounce point, set at a 45 degree angle to the first.

At the second bounce point, the whole thing is moving forward. Repeat for the length of the cylinder. Because the photons are hitting at an angle, the cylinder might start rotating as well as moving forward, but I don't see that as a major issue. At the end of the cylinder, the photons hit a shaped surface and bounce back along the tubes center and out into space.

Did a bit of reading on laser propulsion systems. A Doctor Bae ran some laboratory tests on this: bouncing laser beams multiplied the 'thrust' by a factor of 3000+ - into EM Drive territory without the physics headache. He proposed two linked spacecraft, with laser beams between them, something NASA is supposed to be looking into for near earth applications. My idea is one spacecraft (the cylinder) and a multiplier of about 1500, if the cylinder is long enough. Not sure, but that's should be on a par with the Brady EM drive model.

Alter the angles a bit, test different lasers/emitters, might get a lot more work out of the photons, increasing thrust further.

Would this violate the paradox?

You seem to misunderstand the fundamentals of mechanics.

If a photon hits a mirror at a 45 degree angle and reflects off it, the mirror will receive an impulse perpendicular to the plane of the mirror only. It will not be pushed in the direction of the other component of the photon at all.

It's not just with photons. If you have a billiard ball and you bounce it off another billiard ball that was stationary so that the original ball end up leaving at a 90 degree angle to its initial direction of travel, the other ball will end up traveling at a 45 degree angle to the path of the original ball.

It's non-intuitive because our intuition is shaped by friction tending to pull things along, but such friction is not a part of purely elastic collisions, and photons bouncing off mirrors are purely elastic.

So, every time your photon bounces off the wall, the momentum it imparts will only be to push outward perpendicular to the axis of the tube. And it will be cancelled by the next bounce off the opposite wall.

The only effect of the net momentum of the tube is the opposite of whatever momentum the photo has when it finally leaves the tube. Whatever it does as it bounces around in the tube will have no net effect.

First, note that the evanescent wave (7) possesses longitudinal canonical momentum pOz∝kz>k, which exceeds the momentum of a plane wave with the same local intensity.

That's what led me to look in this direction. Evanescent waves exhibit unusual behavior. The answer to your question then is that the photon rocket is not the ultimate in efficiency. Make a photon rocket using evanescent wave photons and the efficiency will be higher.

First, note that the evanescent wave (7) possesses longitudinal canonical momentum pOz∝kz>k, which exceeds the momentum of a plane wave with the same local intensity.

That's what led me to look in this direction. Evanescent waves exhibit unusual behavior. The answer to your question then is that the photon rocket is not the ultimate in efficiency. Make a photon rocket using evanescent wave photons and the efficiency will be higher.

What remains unclear is how the linked paper -by itself- addresses the issue of conservation of momentum of an EM Drive: I do not recall the linked paper specifically addressing conservation of momentum of an EM Drive cavity where all the microwave photons remain inside the cavity. If it is claimed that the evanescent waves (resulting from exponentially-decaying solutions to the electromagnetic field inside cavity) cause the EM Drive (and spacecraft) to accelerate, what balances the change in the EM Drive (and the spacecraft’s) momentum?.

So the question remains: what balances the momentum change of an EM Drive accelerated by evanescent waves? Are you proposing an interaction with the Quantum Vacuum? or terms coupling electromagnetism with gravitational forces? or something else?

In relativity; coupling of gravity and electromagnetism is infinitesimal though. That's what got Martin Tajmar's experiment so much attention at first. It suggested gravity-EM coupling billions of times stronger than predicted by RT. and what he got was still extremely tiny too.

Of course later he attributed his results to air currents caused by his cryo-coolant sublimating and retracted his paper.

Parenthetically, Tajmar's general design was also used by Ning Li and Podkletnov but probably differed in the details of cooling and method of obtaining rotation and materials for the disks.

That branch (family?) of gravity-EM drive designs has had bad luck even though there may be something there. Tajmar retracted, Ning Li allegedly absconded with research funds, Podkletnov got the kook treatment and retreated to Russia where he continues to claim results.

EDIT: in other news a recent experiment designed to test spin gravity failed to detect any difference in gravitation effects on a particle with a zero spin value and a non zero spin value. fermion and bosons were used...

In relativity; coupling of gravity and electromagnetism is infinitesimal though. That's what got Martin Tajmar's experiment so much attention at first. It suggested gravity-EM coupling billions of times stronger than predicted by RT. and what he got was still extremely tiny too.

Of course later he attributed his results to air currents caused by his cryo-coolant sublimating and retracted his paper.

Parenthetically, Tajmar's general design was also used by Ning Li and Podkletnov but probably differed in the details of cooling and method of obtaining rotation and materials for the disks.

That branch (family?) of gravity-EM drive designs has had bad luck even though there may be something there. Tajmar retracted, Ning Li allegedly absconded with research funds, Podkletnov got the kook treatment and retreated to Russia where he continues to claim results.

EDIT: in other news a recent experiment designed to test spin gravity failed to detect any difference in gravitation effects on a particle with a zero spin value and a non zero spin value. fermion and bosons were used...

So the question remains: what balances the momentum change of an EM Drive accelerated by evanescent waves? Are you proposing an interaction with the Quantum Vacuum? or terms coupling electromagnetism with gravitational forces? or something else?

No - I am proposing that electromagnetic wave momentum depends on group velocity, and that evanescent waves in these circumstances exhibit superluminal group velocity. Nothing is violated - wave momentum reacts against the base plate and energy is inductively drawn from the cavity.

I'll challange you, Dr. Rodel, and Mathematica to demonstrate why/how the energy resolves from the subluminal velocity solution of wave equations. I can help you formulate the problem but we need independent confirmation and you have shown great capability with Mathematica. Do that and you will have solved the EM drive paradox.

So the question remains: what balances the momentum change of an EM Drive accelerated by evanescent waves? Are you proposing an interaction with the Quantum Vacuum? or terms coupling electromagnetism with gravitational forces? or something else?

No - I am proposing that electromagnetic wave momentum depends on group velocity, and that evanescent waves in these circumstances exhibit superluminal group velocity. Nothing is violated - wave momentum reacts against the base plate and energy is inductively drawn from the cavity.

I'll challange you, Dr. Rodel, and Mathematica to demonstrate why/how the energy resolves from the subluminal velocity solution of wave equations. I can help you formulate the problem but we need independent confirmation and you have shown great capability with Mathematica. Do that and you will have solved the EM drive paradox.

But evanescent waves decay exponentially. If you enclose the whole device in a large (imaginary) box, everything coming out will be just regular plane waves with well-known momentum. So where's the extra momentum coming from?

So the question remains: what balances the momentum change of an EM Drive accelerated by evanescent waves? Are you proposing an interaction with the Quantum Vacuum? or terms coupling electromagnetism with gravitational forces? or something else?

No - I am proposing that electromagnetic wave momentum depends on group velocity, and that evanescent waves in these circumstances exhibit superluminal group velocity. Nothing is violated - wave momentum reacts against the base plate and energy is inductively drawn from the cavity.

I'll challange you, Dr. Rodel, and Mathematica to demonstrate why/how the energy resolves from the subluminal velocity solution of wave equations. I can help you formulate the problem but we need independent confirmation and you have shown great capability with Mathematica. Do that and you will have solved the EM drive paradox.

But evanescent waves decay exponentially. If you enclose the whole device in a large (imaginary) box, everything coming out will be just regular plane waves with well-known momentum. So where's the extra momentum coming from?

I don't think it matters what happens to the photons after they depart the thruster interface. An analogy would be the classic photon rocket, or a chemical rocket engine.

A chemical rocket leaves the launch pad but the momentum of the exhaust gas is immediately diverted. The rocket still works. Same thing for a photon rocket, it doesn't matter if the expelled photon beam strikes a planetary body, a mirror or is adsorbed by a dust cloud, the rocket still works. The same rule should hold for evanescent waves.

Meanwhile, I gather there are at least two other labs (besides NASA, Yang Juan and Shawyer) working with cavity-type EmDrives. Anyone heard anything? Do we know what Boeing did after testing the one Shawyer sent them? They say they are not working with him, but that doesn't rule out developing his technology.